A perturbation-based stochastic nonlinear beam element formulation using the B-spline wavelet on the interval finite element method

Vadlamani, S and Arun, CO (2021) A perturbation-based stochastic nonlinear beam element formulation using the B-spline wavelet on the interval finite element method. In: Acta Mechanica .

PDF act_mec_2021.pdf - Published Version Restricted to Registered users only Download (1MB) | Request a copy

Abstract

The current work presents a formulation of stochastic B-spline wavelet on the interval (BSWI)-based wavelet finite element method (WFEM) for analysis of beams incorporating von Kármán nonlinear strains. The spatial variation of the modulus of elasticity is modelled as a homogeneous random field. The proposed formulation is given for both Euler�Bernoulli beam theory and Timoshenko beam theory. For the discretization of both random field and response, BSWI scaling functions are used. A set of three nonlinear equations is derived based on the perturbation approach for evaluating the derivatives of the field variable with respect to random variables. Numerical examples under different boundary conditions based on the proposed formulations are solved and compared with solutions obtained from Monte Carlo simulation (MCS). The effect of the coefficient of variation and correlation length parameter on the response statistics is examined. In addition, a comparison of normalized computational times obtained from the perturbation approach and MCS is carried out. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

Item Type:	Journal Article
Publication:	Acta Mechanica
Publisher:	Springer
Additional Information:	The copyright for this article belongs to Springer
Keywords:	Computation theory; Continuum mechanics; Finite element method; Intelligent systems; Interpolation; Nonlinear equations; Stochastic systems, 'current; B-spline wavelet on the intervals; Beam elements; Element formulation; Interval finite elements; Monte Carlo's simulation; Non-linear beams; Perturbation approach; Random fields; Stochastics, Monte Carlo methods
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	13 Dec 2021 11:39
Last Modified:	13 Dec 2021 11:39
URI:	http://eprints.iisc.ac.in/id/eprint/70762

Actions (login required)

View Item